Vanessa Kosoy comments on A Solomonoff Inductor Walks Into a Bar: Schelling Points for Communication

[Vanessa Kosoy]

Then: $O($$ϵ+{ϵ}^{\prime }+$log $K\left(x\right)$) $\ge K\left({\Lambda }^{\prime }|\Lambda \right)$.

O-notation in contexts like this is somewhat ambiguous, because it’s not clear what is treated as a constant and what is treated as a variable that grows to infinity. Would it be correct to say that there exist constants $A,B>0$ that depend on nothing except for the implicit choice of UTM (or maybe they also need to depend on $TM$?) s.t.

$$K\left({\Lambda }^{\prime }|\Lambda \right)\le A(ϵ+{ϵ}^{\prime }+\log K(x\left)\right)+B$$

[johnswentworth]

Yes. In fact, IIRC only B depends on the choice of UTM, A can be a universal constant.